Non-full-length bonding type anchor cable slip expansion stage stress distribution calculation method and system

Abstract

The invention provides a non-full-length bonding type anchor cable slip expansion stage stress distribution calculation method and system, and relates to the technical field of anchor cable supporting, and the method comprises the steps: analyzing the stress of a non-full-length bonding type anchor cable in a drawing process, and considering the influence of a free section grouting body on an anchor cable system load transmission mode; constructing a mechanical equilibrium differential equation of anchor cable load transmission; analyzing the tangential stress state of the slurry-soil interface according to a mechanical equilibrium differential equation; aiming at the inclined anchor cable and the vertical anchor cable, calculating the stress distribution of different types of anchor cables when the slurry-soil interface is in the slip expansion stage based on the tangential stress state of the slurry-soil interface. According to the method, the influence of the grouting body-soil body interface mechanical property in the slippage expansion stage on the anchor rod load transmission rule and stress distribution is considered, and the calculation method has universal applicability.

Description

Technical Field

[0001] The present invention relates to the technical field of anchor cable support, and in particular to a method and system for calculating stress distribution in a non-full-length bonded anchor cable sliding extension stage. Background Art

[0002] The statements in this section merely provide background information related to the present disclosure and do not necessarily constitute prior art.

[0003] Soil anchoring technology has shown unique advantages in the field of geotechnical engineering due to its efficient soil reinforcement effect, simple and fast construction process and relatively low economic cost. It is widely used in deep foundation pits, slopes and tunnels and other projects. It has good deformation control ability and can significantly improve the shear strength of rock and soil.

[0004] At present, most studies only study full-length bonded anchors, and there are relatively few studies on non-full-length bonded anchors. In addition, only the load transfer mechanism of the anchor section is discussed, ignoring the application distribution law of the free section. The Technical Code for Construction Foundation Pit Support (JGJ 120-2012) requires that the grouting of prestressed anchor cables should be poured to the hole mouth, which means that there is still grouting in the free section of the anchor cable, and there is no bonding stress between the anchor cable tendon and the grouting body, but there is still shear stress transmission at the interface between the grouting body and the soil. It can be seen that the free section grouting body provides a certain axial resistance during the anchor cable pulling process. It is obviously conservative to ignore the contribution of this part in the anchoring effect.

[0005] Due to the complex overall stress of the anchor rod, the bearing capacity of the soil anchor cable is mostly determined by the shear resistance of the slurry-soil interface. In the design of anchor support, most of them use simplified calculation formulas for design and verification according to the specifications, but rarely consider the influence of the mechanical properties of the anchor interface on the support design. In addition, most of the existing research focuses on full-length bonded anchor rods, while there are fewer studies on non-full-length bonded anchor rods, and most of them focus on the load transfer mechanism of the anchoring section, ignoring the stress distribution of the free section; therefore, there is a lack of a solution to study the load transfer mechanism and stress distribution calculation of non-full-length bonded anchor cables. Summary of the invention

[0006] In order to solve the above problems, the present invention proposes a method and system for calculating the stress distribution of non-full-length bonded anchor cables in the slip extension stage, introduces the slip extension stage, describes the state when the slurry-soil interface produces a plastic zone but has not fully entered the plastic stage, considers the mechanical properties of the grouting body-soil interface in the slip extension stage, and solves the stress distribution of the slurry-soil interface in the slip extension stage for two arrangements of inclined anchor cables and vertical anchor cables, respectively, to provide a basis for later optimization of design parameters, evaluation of bearing capacity and improvement of long-term stability.

[0007] According to some embodiments, the present disclosure adopts the following technical solutions:

[0008] The calculation method of stress distribution in the sliding extension stage of non-full-length bonded anchor cable includes:

[0009] The stress of the non-full-length bonded anchor cable is analyzed, the influence of the anchor section grouting and the free section grouting on the load transfer mode of the anchor cable system is considered, and the mechanical equilibrium differential equation of the load transfer of the non-full-length bonded anchor cable is constructed;

[0010] The tangential stress state of the slurry-soil interface is analyzed according to the test results of the mechanical properties of the slurry-soil interface;

[0011] For inclined anchor cables and vertical anchor cables, based on the mechanical equilibrium differential equation and the tangential stress state of the slurry-soil interface, the stress distribution of different types of anchor cables when the slurry-soil interface is in the sliding extension stage is calculated respectively.

[0012] Among them, by analyzing the normal stress of different types of anchor cables and the stress distribution law of anchor cables in the sliding extension stage, the mechanical equilibrium differential equations in different stress intervals are described according to the elastic and plastic partitions, so as to complete the stress distribution calculation of different types of anchor cables, and analyze the stress distribution of the anchor rod according to the solution results, predict its stress state, and realize the later design parameter optimization and bearing capacity evaluation.

[0013] According to some embodiments, the present disclosure adopts the following technical solutions:

[0014] The stress distribution calculation system of non-full-length bonded anchor cable in the sliding extension stage includes:

[0015] Mathematical model building module, used to analyze the stress of non-full-length bonded anchor cables, consider the influence of anchor section grouting and free section grouting on the load transfer mode of anchor cable system, and build the mechanical equilibrium differential equation of load transfer of non-full-length bonded anchor cables;

[0016] The tangential force analysis module is used to analyze the tangential force state of the slurry-soil interface according to the test results of the mechanical properties of the slurry-soil interface;

[0017] The stress distribution calculation module is used to calculate the stress distribution of different types of anchor cables when the slurry-soil interface is in the sliding extension stage for inclined anchor cables and vertical anchor cables based on the mechanical equilibrium differential equation and the tangential stress state of the slurry-soil interface;

[0018] Among them, by analyzing the normal stress of different types of anchor cables and the stress distribution law of anchor cables in the sliding extension stage, the mechanical equilibrium differential equations in different stress intervals are described according to the elastic and plastic partitions, so as to complete the stress distribution calculation of different types of anchor cables, and analyze the stress distribution of the anchor rod according to the solution results, predict its stress state, and realize the later design parameter optimization and bearing capacity evaluation.

[0019] According to some embodiments, the present disclosure adopts the following technical solutions:

[0020] A computer program product comprises a computer program, wherein when the computer program is executed by a processor, the method for calculating the stress distribution of a non-full-length bonded anchor cable in the sliding extension stage is implemented.

[0021] According to some embodiments, the present disclosure adopts the following technical solutions:

[0022] A non-transitory computer-readable storage medium is used to store computer instructions. When the computer instructions are executed by a processor, the stress distribution calculation method of the non-full-length bonded anchor cable in the sliding extension stage is implemented.

[0023] According to some embodiments, the present disclosure adopts the following technical solutions:

[0024] An electronic device comprises: a processor, a memory and a computer program; wherein the processor is connected to the memory, the computer program is stored in the memory, and when the electronic device is running, the processor executes the computer program stored in the memory so that the electronic device executes the stress distribution calculation method for the sliding extension stage of a non-full-length bonded anchor cable.

[0025] Compared with the prior art, the present invention has the following beneficial effects:

[0026] The method for calculating the stress distribution of a non-full-length bonded anchor cable in the slip extension stage disclosed in the present invention proposes the concept of the slip extension stage, describes the state when the slurry-soil interface produces a plastic zone but has not fully entered the plastic stage, takes the anchor section steel strands and the grouting body into consideration together, and solves the stress distribution of the slurry-soil interface in the slip extension stage for inclined anchor cables and vertical anchor cables, respectively. Compared with the stress distribution solved in the elastic stage, it is more accurate and saves support costs. The calculation method disclosed in the present invention has universal applicability.

[0027] The stress distribution calculation method of the non-full-length bonded anchor cable in the sliding extension stage disclosed in the present invention takes into account the mechanical properties of the grouting body-soil interface in the sliding extension stage. It can be widely applied to different engineering scenarios for the two arrangements of inclined anchor cables and vertical anchor cables, such as the inclined anchor rods commonly used in foundation pit support and the vertical anchor rods widely used in anti-floating design. At the same time, through the calculation results, the stress distribution of the anchor rod is analyzed and its stress state is predicted, which provides a strong scientific basis for the engineering application of anchor cables in sandy soil layers and the prevention and control of engineering disasters, and has important significance and practical application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] The accompanying drawings constituting a part of the present disclosure are used to provide a further understanding of the present disclosure. The illustrative embodiments of the present disclosure and their descriptions are used to explain the present disclosure and do not constitute an improper limitation on the present disclosure.

[0029] Figure 1 It is a schematic diagram of vertical and inclined anchor cables according to an embodiment of the present disclosure;

[0030] Figure 2 A schematic diagram of the stress of a non-full-length bonded anchor cable according to an embodiment of the present disclosure;

[0031] Figure 3 The anchor cable mechanical model of the embodiment of the present disclosure;

[0032] Figure 4 is an ideal line elastoplastic model of the slurry-soil interface according to an embodiment of the present disclosure;

[0033] Figure 5 It is a schematic diagram of the anchor grout-soil interface in the sliding extension stage according to an embodiment of the present disclosure;

[0034] Figure 6 is the free segment length L of the embodiment of the present disclosure f＝ 3m, different anchoring lengths L a (i.e. L a / L f ) pa and L pf The impact of relationships;

[0035] Figure 7 For the embodiment of the present disclosure, a / L f =1, different anchoring section lengths L a (or free segment length L f ) pa and L pf The impact of relationships;

[0036] Figure 8 This is a schematic diagram of the distribution of axial stress, shear stress and displacement of the anchor cable in the sliding extension stage according to an embodiment of the present disclosure;

[0037] Fig. 9 It is a schematic diagram of the axial stress distribution of the steel strand and the grouting body in the anchor cable sliding extension stage according to an embodiment of the present disclosure;

[0038] Fig.10 This is a schematic diagram of the distribution of axial stress, shear stress and displacement in the anchor cable sliding extension stage-S2 of an embodiment of the present disclosure;

[0039] Fig.11 It is a schematic diagram of the distribution of axial stress, shear stress and displacement in the sliding expansion stage of the vertical anchor cable according to an embodiment of the present disclosure. DETAILED DESCRIPTION

[0040] The present disclosure is further described below in conjunction with the accompanying drawings and embodiments.

[0041] It should be noted that the following detailed descriptions are all illustrative and are intended to provide further explanation of the present disclosure. Unless otherwise specified, all technical and scientific terms used herein have the same meanings as those commonly understood by those skilled in the art to which the present disclosure belongs.

[0042] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present disclosure. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprising" and / or "including" are used in this specification, it indicates the presence of features, steps, operations, devices, components and / or combinations thereof.

[0043] Example 1

[0044] In one embodiment of the present disclosure, a method for calculating stress distribution of a non-full-length bonded anchor cable in the sliding extension stage is provided, which takes into account the influence of the mechanical properties of the grouting body-soil body interface in the sliding extension stage on the load transfer law and stress distribution of the anchor rod, and is aimed at two types of anchor cables, namely inclined anchor cables and vertical anchor cables, including:

[0045] Step 1: Analyze the stress of the non-full-length bonded anchor cable, consider the influence of the anchor section grouting and the free section grouting on the load transfer mode of the anchor cable system, and construct the mechanical equilibrium differential equation of the load transfer of the non-full-length bonded anchor cable;

[0046] Step 2: Analyze the tangential stress state of the slurry-soil interface according to the test results of the mechanical properties of the slurry-soil interface;

[0047] Step 3: For inclined anchor cables and vertical anchor cables, based on the mechanical equilibrium differential equation and the tangential stress state of the slurry-soil interface, the stress distribution of different types of anchor cables when the slurry-soil interface is in the slip extension stage is calculated respectively;

[0048] Among them, by analyzing the normal stress of different types of anchor cables and the stress distribution law of anchor cables in the sliding extension stage, the mechanical equilibrium differential equations in different stress intervals are described according to the elastic and plastic partitions, so as to complete the stress distribution calculation of different types of anchor cables, and analyze the stress distribution of the anchor rod according to the solution results, predict its stress state, and realize the later design parameter optimization and bearing capacity evaluation.

[0049] As an embodiment, the stress distribution calculation method of the non-full-length bonded anchor cable in the sliding extension stage of the present invention takes into account the mechanical properties of the grouting body-soil interface in the sliding extension stage, and for two arrangements of inclined anchor cables and vertical anchor cables (such as Figure 1 ), the specific implementation process is as follows:

[0050] Step 1: Analyze the stress of the non-full-length bonded anchor cable, consider the influence of the anchor section grouting and the free section grouting on the load transfer mode of the anchor cable system, and construct the mechanical equilibrium differential equation of the load transfer of the non-full-length bonded anchor cable;

[0051] Specifically, the failure mode in which the anchor cable and the grouting body are pulled out together is more common in soil anchors. When the soil layer on the surface of the anchor has sufficient restraint, the anchor cable slips and fails along the grout-soil interface. The stress of the non-full-length bonded anchor cable during the pulling process is analyzed, and a load transfer mechanical model of the non-full-length bonded anchor cable is constructed. Based on the load transfer mechanical model of the non-full-length bonded anchor cable, a mathematical model of anchor cable load transfer is constructed. The load transfer mechanical model of the non-full-length bonded anchor cable is shown in Figure 2 The load transfer mechanism is that the tension anchoring bar (steel strand or steel bar) in the center is transferred to the grouting body through the bonding force of the rod-grout interface, and then transferred to the soil layer through the bonding force of the grouting body-soil interface. f is the free segment length, m; L a is the length of the anchoring section, m; D is the diameter of the grouting body; F is the tension.

[0052] Among them, the mathematical model of anchor load transfer adopts the following assumptions:

[0053] 1) Since the actual deformation of the interaction between the anchor cable and the soil is very complex, it is decomposed into two components along the axis of the anchor cable and perpendicular to the axis of the anchor cable, and it is assumed that the two components are independent of each other;

[0054] 2) No debonding failure occurs at the rod-slurry interface;

[0055] 3) Use nonlinear springs to simulate the shear behavior of the slurry-soil interface.

[0056] Furthermore, according to the load transfer mechanical model of non-full-length bonded anchor cables, considering that the slurry-sand stone body often does not produce overall damage during the sliding shear process, the influence of the anchoring section grouting body and the free section grouting body on the load transfer mode of the anchor cable system is considered, and the differential equations of the mechanical equilibrium relationship of the anchoring section and the free section are obtained respectively for the anchoring section grouting body and the free section grouting body. Specifically:

[0057] Since the bond strength between the rod and the grout in the anchor section is often higher than that between the grout and the soil, the steel strands in the anchor section are considered together with the grouting body. Figure 3As shown. The coordinate system takes O as the origin, and the AC direction is the positive direction of the x-axis. Considering that the mortar-sand-stone body often does not produce overall damage during the sliding shear process, it is included in the calculation radius of the anchor body, and the calculation radius is from the outer edge of the mortar-sand-stone body to the axis of the anchor body. According to the mechanical equilibrium relationship of the micro-element of the anchoring section, it can be obtained:

[0058]

[0059] In the formula, u a (x) is the displacement of the grouting body in the anchoring section, in m; E a is the equivalent elastic modulus of the anchoring section, in GPa; A a Calculate the cross-sectional area of ​​the anchoring section in mm 2 ; E g is the elastic modulus of the grouting body, in GPa; A g is the cross-sectional area of ​​the grouting body, in mm 2 ; E mix is the elastic modulus of the mortar-sand stone body, in GPa; A mix is the cross-sectional area of ​​the slurry-sand stone body, in mm2; D c D is the calculated diameter of the grouting body in m. c =D+2t mix ;t mix is the thickness of the slurry-sand stone body, in m; τ gs (x) is the shear stress at the slurry-soil interface, in kPa; L a is the length of the anchoring section, in meters. s A is the elastic modulus of the steel strand, MPa; s is the cross-sectional area of ​​the steel strand, mm 2 .

[0060] Afterwards, considering the influence of the free section grouting on the load transfer mode of the anchor cable system, the free section grouting is taken as a microelement segment, and according to the mechanical equilibrium relationship, it can be obtained:

[0061]

[0062] In the formula, u fg (x) is the displacement of the free section grouting body, in m; E fg is the elastic modulus of the free segment anchor, in GPa; A fg is the cross-sectional area of ​​the free segment anchor, in mm 2 , A fg =A g +A mix ;

[0063] The displacement of the grouting body can be expressed as:

[0064]

[0065] In the formula, u gs (x) is the shear deformation of the slurry-soil interface, in m; u soil (x) is the shear deformation of the soil, in m.

[0066] The shear deformation of the slurry-soil interface during the shear process is mainly concentrated in the "shear slip zone", and the soil deformation outside the "shear slip zone" is small. gs It plays a controlling role in the displacement of the grouting body. To simplify the calculation, the shear deformation of the soil is ignored. soil .

[0067] The axial stress in the grouting body (or anchor body) can be obtained according to the physical equation:

[0068]

[0069] In the formula, σ a is the average axial stress of the grouting body and the steel strand in the anchoring section, kPa; σ fg is the axial stress of the free section grouting body, kPa.

[0070] Step 2: Analyze the tangential stress state of the slurry-soil interface according to the test results of the mechanical properties of the slurry-soil interface;

[0071] According to the test results of the mechanical properties of the slurry-soil interface, that is, the shear characteristics of the slurry-soil interface, the shear mechanics relationship of the slurry-soil interface is obtained. The shear mechanics relationship of the slurry-soil interface is assumed to be an ideal line elastoplastic model, the shear failure strength formula of the slurry-soil interface is defined, and the tangential stress state of the slurry-soil interface is obtained.

[0072] Specifically, according to the test results of mechanical properties of slurry-soil interface, the slurry-soil interface conforms to the hyperbolic shear stress and displacement relationship, such as Figure 3 As shown. Since τ gs with u gs The hyperbolic function form is not convenient for solving the subsequent stress and deformation analytical functions. Under the premise of not affecting the anchor load transfer law, a certain degree of simplification is performed. The shear mechanics relationship of the slurry-soil interface is assumed to be an ideal line elastic-plastic model, as shown in 4. Its expression can be expressed as:

[0073] τ gs =k gsi u gs (7)

[0074] In the formula, τ gs is the shear stress at the slurry-soil interface, kPa; k gsi is the reference initial shear stiffness of the slurry-soil interface, kPa / m.

[0075] The shear failure strength of the slurry-soil interface can be defined as:

[0076] τ gsf =σ n tanθ gs +c gs (8)

[0077] In the formula, τ gsf is the shear failure strength of the slurry-soil interface, kPa; θ gs is the friction angle of the slurry-soil interface, °; c gs is the slurry-soil interface bonding force, kPa; σ n is the interface normal stress, kPa.

[0078] Step 3: For inclined anchor cables and vertical anchor cables, based on the mechanical equilibrium differential equation and the tangential stress state of the slurry-soil interface, the stress distribution of different types of anchor cables when the slurry-soil interface is in the slip extension stage is calculated respectively;

[0079] First, the slip extension stage of the slurry-soil interface is defined as follows: as the axial load continues to increase, the shear stress of the slurry-soil interface continues to increase. The maximum shear stress of the slurry-soil interface of the non-full-length bonded anchor appears at the junction of the free section and the anchor section, and decreases monotonically toward both ends of the anchor. When the maximum shear stress of the interface exceeds its shear failure strength, the interface enters a plastic state. The plastic zone develops toward both ends of the anchor as the axial load increases. The state when the slurry-soil interface produces a plastic zone but has not fully entered the plastic stage is called the slip extension stage. Figure 5 As shown in the figure, the slurry-soil interface in the AD and EC segments is in an elastic state, and the interface in the DE segment is in a plastic state. a is the length of the anchoring section, m; L f is the length of the free segment, m; L ea is the length of the elastic zone of the anchoring section, m; L pa is the length of the plastic zone of the anchoring section, m; L pf is the length of the plastic zone of the free segment, m; L ef is the length of the elastic zone of the free segment, m.

[0080] Secondly, by analyzing the normal stress of different types of anchor cables and the stress distribution law of anchor cables in the sliding extension stage, the mechanical equilibrium differential equations in different stress intervals are described according to the elastic and plastic partitions, so as to complete the stress distribution calculation of different types of anchor cables, and carry out support design according to the obtained stress distribution.

[0081] Specifically, considering the different normal stresses of anchor cables with different layout types, the stress distribution laws of two types of anchor cables, inclined anchor cables and vertical anchor cables, during the slip extension stage are described separately.

[0082] 1) If Figure 1In (a), the inclined anchor cable has sufficient burial depth and belongs to a deep buried structure. The normal stress of different sections does not change with the position. Then the shear failure strength of the slurry-soil interface of different sections of the anchor cable is τ gsf Keep constant, and describe the mechanical equilibrium relationship of different stress intervals according to the elastic and plastic partitions, that is, combine (1) and (3) with (7), and describe the mechanical equilibrium relationship of different stress intervals according to the elastic and plastic partitions:

[0083]

[0084] Solving the differential equation of formula (9) yields the axial displacement of the anchor cable at different positions during the sliding extension stage:

[0085]

[0086] In the formula, α, β—simplification coefficients, R1~R8 are the unknown coefficients of the differential equation.

[0087] The axial stress boundary conditions at points A and C and the shear stress boundary conditions at points D and E can be obtained from the continuity conditions of the forces at each interface:

[0088] σ a (x) x＝0 =0,

[0089]

[0090] Substituting the boundary conditions into the displacement equations of the AD segment and the EC segment in equations (6) and (10), R1, R2, R7 and R8 can be directly solved as follows:

[0091]

[0092] According to the continuity conditions of the axial stress at points D and E, the following boundary conditions can be obtained:

[0093]

[0094] Substituting the above boundary conditions into equations (6) and (10), we can obtain R3 and R5:

[0095]

[0096] According to the deformation continuity conditions at points D and E, the following boundary conditions can be obtained:

[0097]

[0098] Substituting the above boundary conditions into equation (10) yields R4 and R6:

[0099]

[0100] The undetermined coefficients R1 to R8 have all been determined.

[0101] To determine the stress distribution and load transfer law of the entire anchor cable, it is necessary to determine the length L of the plastic zone. pa and L pf . Introduce the continuity conditions of point B displacement and axial stress:

[0102]

[0103] Substituting the above boundary conditions into equations (6) and (10), we can assume

[0104] A3=πD c τ gsf , We can get:

[0105]

[0106] A1tanh(αL ea )+A2tanh(βL ef )+A3(L pa +L pf )=F(12)

[0107] The variable L in equations (11) and (12) is pa and L pf The expression form is complex and it is difficult to find its analytical function. This paper uses Matlab to calculate the numerical solution of equations (11) and (12) to try to find L pa and L pf Based on the field measured data, L pa and L pf The functional relationship of the anchor length L and the influence of different parameters are analyzed. The basic parameters of the anchor cable used in the calculation are shown in Table 1. Based on the basic calculation model, the control variable method is used to study the anchor length L a , L a / L f Shear failure strength of slurry-soil interface τ gsf The influence of other parameters.

[0108] Table 1 Basic parameters of anchor cables

[0109]

[0110] Figure 6 The free section length L is shown f =3m, different anchoring lengths L a (i.e. La / L f ) pa and L pf The influence of the relationship. As can be seen from the figure, as L a The increase of L pf / L pa The value gradually increases. At the same time, it can be seen that when the plastic zone length is small, L pf With L pa It is a linear relationship. When the length of the plastic zone exceeds a certain value, L pf With L pa The slope of the curve changes and no longer satisfies the linear relationship. But overall, L pf With L pa The linear relationship is good. The calculation results of different anchor lengths are linearly fitted, and the correlation coefficient R is greater than 0.98, and the linear fitting characteristics are significant. pf / L pa With L a / L f The two are in a parabolic function relationship, L pf / L pa The range of variation is 0.4-1.0. When L a / L f >1.3, L pf / L pa Approaching 1.

[0111] Figure 7 As shown in the figure, when L a / L f =1, different anchoring section lengths L a (or free segment length L f ) pa and L pf The influence of the relationship. As can be seen from the figure, as L a (L f ) increases, L pf / L pa The value gradually increases, but the impact is relatively small. Similarly, a linear fit is performed on the calculated results, L pf / L pa The range of variation is 0.65-0.85. It can be seen that L a (L f ) and L pf / L pa The value is a cubic polynomial function. When L a (L f )>6m, L pf / L pa Becoming stable.

[0112] After calculation, the shear failure strength of the slurry-soil interface τ gsf Will not affect L pf With L pa , which only affects the corresponding tension F at the same slip extension stage.

[0113] According to the above analysis, L pf and L pa Can be simplified into a linear relationship, which can be expressed as: L pf =a p L pa , where a p is the proportional coefficient. When the anchor cable parameter size is fixed, a p To determine the value.

[0114] By combining equations (6) and (10), the axial stress at the slurry-soil interface during the sliding extension stage of the inclined anchor cable can be obtained:

[0115]

[0116] By combining equations (1) and (3) with (10), the shear stress at the slurry-soil interface during the sliding extension stage of the inclined anchor cable can be obtained:

[0117]

[0118] At this point, the expressions of the average axial stress of the anchor cable, the shear stress at the slurry-soil interface and the axial displacement in the sliding extension stage can be obtained, and their distribution diagrams are shown in the figure below: Figure 8 shown.

[0119] Due to the large difference in strength between the steel strand and the grouting body in the anchor body, the stress distribution between the two is more important. In view of this, this paper studies the load transfer law in the anchoring section through the mechanical equilibrium relationship between the grouting body and the steel strand in the anchoring section. Considering that the rod-slurry interface often has a high shear strength, according to the test results of the mechanical properties of the rod-slurry interface, the shear stress and displacement of the rod-slurry interface are regarded as a linear elastic function relationship. According to the stress equilibrium relationship of the steel strand in the anchoring section, it can be obtained:

[0120]

[0121] τ gt (x) = k gti [u s (x)-u ag (x)]0≤x≤L a (16)

[0122] In the formula, σ s (x) is the axial stress of the steel strand, kPa; D s is the diameter of the steel strand, m; τ gt(x) is the shear stress at the rod-paddle interface, kPa; k gti is the reference initial shear stiffness of the rod-paddle interface, kPa / m; u s (x) is the displacement of the steel strand in the anchoring section, m; u ag (x) is the displacement of the grouting body in the anchoring section, m.

[0123] The stress balance relationship of the grouting body in the anchoring section can be obtained:

[0124]

[0125] In the formula, σ ag (x) is the axial stress of the grouting body in the anchoring section, kPa.

[0126] The axial stress of the grouting body and the steel strand in the anchoring section can be obtained according to the physical equation:

[0127]

[0128] Substituting equation (16) and equation (19) into equation (15), we can get the differential equation:

[0129]

[0130] Based on the average displacement and axial stress of the anchor body of the anchor cable, the load transfer law of the anchor body and the steel strand in the anchor section is studied through the mechanical equilibrium relationship between the grouting body and the steel strand in the anchor section. The stress equilibrium equation and physical equation of the steel strand in the anchor section can refer to equations (16), (19) and (15), and the differential equation (20) can be obtained by combining them. The stress equilibrium equation and physical equation of the grouting body can refer to equations (17) and (18). Since the grout-soil interface enters the slip extension stage, the AD section and the DB section need to be considered separately. The differential equation can be expressed as follows:

[0131]

[0132] Combining equations (20) and (21), we can get s (x) and u ag (x) is a non-homogeneous linear differential equation system, and M = E s A s E fg A fg / (πD s k gti ), N=E a A a ,set up C″=πD c τ gsf , we can solve the differential equations:

[0133]

[0134]

[0135] In the formula, C1′~C4′, C1″~C4″ are the unknown coefficients of the differential equation.

[0136] According to the stress and deformation continuity conditions of the anchor bolt anchoring section, it is not difficult to obtain the following boundary conditions:

[0137] Point B:

[0138] Point D:

[0139] Point A: u′ ag (x)E fg | x＝0 =0,u′ s (x)E s | x＝0 =0

[0140] Combining equations (22) and (23) with boundary conditions, the unknown coefficients of eight differential equations can be determined:

[0141]

[0142]

[0143] In the above analysis of the slip extension stage of the anchor cable, both the free section and the anchor section of the anchor cable contain elastic zones. To facilitate the distinction between different loading stages, this stage can be called the slip extension stage-S1. When the axial force continues to increase, due to the different lengths and plastic zone ratios of the anchor section and the free section, the anchor section and the free section cannot enter the fully plastic stage at the same time. This loading stage is called the slip extension stage-S2.

[0144] In view of this, taking the case where the slurry-soil interface in the anchoring section first enters the fully plastic stage and the slurry-soil interface in the free section is in the slip extension stage as an example, the axial stress and deformation law of the anchor cable in the slip extension stage-S2 are analyzed. Formulas (1) and (3) are combined with formula (7), and the mechanical equilibrium relationship in different force intervals is described according to the elastic and plastic partitions:

[0145]

[0146] Solving the differential equation of formula (24) yields:

[0147]

[0148] In the formula, R1′~R6′ are the unknown coefficients of the differential equation.

[0149] According to the stress and displacement boundary conditions at points A, B, E and C, we can obtain:

[0150]

[0151] σ a (x)| x＝0 =0,

[0152] Substituting the above boundary conditions into equation (25) yields:

[0153] R′1=0

[0154]

[0155]

[0156] According to the derived formula for the axial displacement of the anchor cable, the stress state of the free section of the anchor cable grouting body is completely consistent with the slip extension stage - S1. Fig.10 The figure shows the distribution diagram of the axial displacement, average axial stress and shear stress of the slurry-soil interface of the anchor cable. It can be seen that the slurry-soil interface of the anchor section has entered the fully plastic stage, the average axial stress of the anchor section is distributed in a straight line along the anchor section, and the displacement is a parabolic curve.

[0157] Since the grout-soil interface in the anchoring section enters the fully plastic stage, the differential equation of the grouting body can be expressed as follows:

[0158]

[0159] Combining equations (20) and (26), we can get s (x) and u ag (x) can be solved to obtain the following non-homogeneous linear differential equations:

[0160]

[0161] The coefficients of the equation group are determined according to the boundary conditions of the anchoring section. Here, the solution results of the unknown coefficients are given directly:

[0162]

[0163] C″′4=0

[0164] It can be seen from the calculation formula that the axial stress distribution law of the grouting body and the steel strand in the slip extension stage-S2 is similar to that in the slip extension stage-S1, which will not be repeated here.

[0165] 2) Vertical anchor cable

[0166] For vertical anchor cables (see Figure 1b) The burial depth of different sections along the axial direction is different, and the normal soil pressure increases with the depth. Since the normal soil pressure is proportional to the burial depth, and the lateral pressure coefficient is related to the construction process and the anchor loading method, the normal stress of the anchor slurry-soil interface can be expressed as:

[0167] σ n =σ ne +σ nd =K0γz+σ nd (28)

[0168] In the formula, σ ne is the static soil pressure (before loading), kPa; σ nd is the horizontal stress generated by soil volume change during loading, kPa; K0 is the static earth pressure coefficient; z is the burial depth, m.

[0169] This disclosure assumes that the normal stress of the vertical anchor cable remains constant during the pulling process, and ignores the change in soil pressure caused by volume change. Therefore, the normal force of the slurry-soil interface per unit length of the anchor cable can be expressed as:

[0170] N n =πDσ ne =πDK0γz(29)

[0171] Combining equations (8) and (29) we can obtain the shear failure strength τ of different cross sections of the anchor cable: gsf Similarly, taking the end of the anchoring section as the origin and the direction of the free section of the anchor cable as the positive x direction, we can get τ gsf expression:

[0172] τ gsf =K0γ(L a +L f -x)tanθ gs +c gs (30)

[0173] K0 is the static earth pressure coefficient; z is the burial depth, m; γ is the soil density, kN / m 3 .

[0174] According to the elastic and plastic partitions, the mechanical equilibrium relationship in different intervals is as follows:

[0175]

[0176] Solve the differential equation by combining equations (30) and (31), and let a = k0γtanθ gs , b = k0γtanθ gs (L a +L f )+c gs , we can get:

[0177]

[0178] In the formula, R1~R8 are the unknown coefficients of the differential equation.

[0179] The axial stress boundary conditions at points A and C and the shear stress boundary conditions at points D and E can be obtained from the continuity conditions of the forces at each interface:

[0180] σ a (x)| x＝0 =0,

[0181]

[0182] Substituting the boundary conditions into the displacement equations of the AD segment and the EC segment in equations (6) and (32), R1, R2, R7 and R8 can be directly solved as follows:

[0183]

[0184]

[0185] According to the continuity conditions of the axial stress at points D and E, the following boundary conditions can be obtained:

[0186]

[0187] Substituting the above boundary conditions into equations (6) and (32), we can obtain R3 and R5:

[0188]

[0189] According to the deformation continuity conditions at points D and E, the following boundary conditions can be obtained:

[0190]

[0191] Substituting the above boundary conditions into equation (32) yields R4 and R6:

[0192]

[0193] Vertical anchor cable L pf and L pa It can also be simplified into a linear relationship, expressed as: L pf =a p L pa .

[0194] By combining equations (6) and (32), the average axial stress at the slurry-soil interface during the sliding extension stage of the vertical anchor cable can be obtained:

[0195]

[0196] By combining equations (1), (3) and (32), the shear stress at the slurry-soil interface during the sliding extension stage of the vertical anchor cable can be obtained:

[0197]

[0198] At this point, the expressions of the average axial stress of the anchor cable, the shear stress at the slurry-soil interface and the axial displacement in the sliding extension stage can be obtained, and their distribution diagrams are shown in the figure below: Fig.11 The final solution process is consistent with the inclined anchor cable calculation process and will not be repeated here.

[0199] At this point, the axial stress and shear stress of the two types of non-full-length bonded anchor cables at the grouting-soil interface in the slip extension stage have been solved. Based on the solution results, the stress distribution of the anchor can be analyzed and its stress state can be predicted, providing a basis for optimizing design parameters, evaluating bearing capacity, and improving long-term stability.

[0200] Example 2

[0201] In one embodiment of the present disclosure, a stress distribution calculation system for a non-full-length bonded anchor cable in a sliding extension stage is provided, comprising:

[0202] Mathematical model building module, used to analyze the stress of non-full-length bonded anchor cables, consider the influence of anchor section grouting and free section grouting on the load transfer mode of anchor cable system, and build the mechanical equilibrium differential equation of load transfer of non-full-length bonded anchor cables;

[0203] The tangential force analysis module is used to analyze the tangential force state of the slurry-soil interface according to the test results of the mechanical properties of the slurry-soil interface;

[0204] The stress distribution calculation module is used to calculate the stress distribution of different types of anchor cables when the slurry-soil interface is in the sliding extension stage for inclined anchor cables and vertical anchor cables based on the mechanical equilibrium differential equation and the tangential stress state of the slurry-soil interface;

[0205] Among them, by analyzing the normal stress of different types of anchor cables and the stress distribution law of anchor cables in the sliding extension stage, the mechanical equilibrium differential equations in different stress intervals are described according to the elastic and plastic partitions, so as to complete the stress distribution calculation of different types of anchor cables, and analyze the stress distribution of the anchor rod according to the solution results, predict its stress state, and realize the later design parameter optimization and bearing capacity evaluation.

[0206] Example 3

[0207] In one embodiment of the present disclosure, a computer program product is provided, including a computer program, which, when executed by a processor, implements the method for calculating stress distribution in the sliding extension stage of a non-full-length bonded anchor cable.

[0208] Example 4

[0209] In one embodiment of the present disclosure, a non-transitory computer-readable storage medium is provided, wherein the non-transitory computer-readable storage medium is used to store computer instructions. When the computer instructions are executed by a processor, the stress distribution calculation method of the non-full-length bonded anchor cable in the sliding extension stage is implemented.

[0210] Example 5

[0211] In one embodiment of the present disclosure, an electronic device is provided, including: a processor, a memory, and a computer program; wherein the processor is connected to the memory, and the computer program is stored in the memory. When the electronic device is running, the processor executes the computer program stored in the memory, so that the electronic device executes the stress distribution calculation method for the sliding extension stage of the non-full-length bonded anchor cable.

[0212] The present disclosure is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present disclosure. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0213] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0214] Although the above describes the specific implementation methods of the present disclosure in conjunction with the accompanying drawings, it is not intended to limit the scope of protection of the present disclosure. Technical personnel in the relevant field should understand that on the basis of the technical solution of the present disclosure, various modifications or variations that can be made by those skilled in the art without creative work are still within the scope of protection of the present disclosure.

Claims

1. The method for calculating the stress distribution of non-full-length bonded anchor cables during the sliding extension stage is characterized by: include: The stress of the non-full-length bonded anchor cable is analyzed, the influence of the anchor section grouting and the free section grouting on the load transfer mode of the anchor cable system is considered, and the mechanical equilibrium differential equation of the load transfer of the non-full-length bonded anchor cable is constructed; The tangential stress state of the slurry-soil interface is analyzed according to the test results of the mechanical properties of the slurry-soil interface; For inclined anchor cables and vertical anchor cables, based on the mechanical equilibrium differential equation and the tangential stress state of the slurry-soil interface, the stress distribution of different types of anchor cables when the slurry-soil interface is in the sliding extension stage is calculated respectively. Among them, by analyzing the normal stress of different types of anchor cables and the stress distribution law of anchor cables in the sliding extension stage, the mechanical equilibrium differential equations in different stress intervals are described according to the elastic and plastic partitions, so as to complete the stress distribution calculation of different types of anchor cables, and analyze the stress distribution of the anchor rod according to the solution results, predict its stress state, and realize the later design parameter optimization and bearing capacity evaluation.

2. The method for calculating stress distribution of a non-full-length bonded anchor cable during the sliding extension phase according to claim 1, characterized in that: The process of constructing the mechanical equilibrium differential equation of load transfer for non-full-length bonded anchor cables is as follows: The stress of non-full-length bonded anchor cables during pulling process is analyzed, and a load transfer mechanical model of non-full-length bonded anchor cables is constructed. According to the load transfer mechanical model of non-full-length bonded anchor cables, a mathematical model of anchor cable load transfer is constructed. The assumptions of the mathematical model of anchor cable load transfer include: 1) the mutual decomposition between the anchor cable and the soil is into two components along the axis of the anchor cable and perpendicular to the axis of the anchor cable, and the two components are assumed to be independent of each other; 2) no debonding failure occurs at the rod-slurry interface; 3) the shear behavior of the slurry-soil interface is simulated using nonlinear springs.

3. The method for calculating stress distribution of a non-full-length bonded anchor cable during the sliding extension stage according to claim 2, characterized in that: According to the load transfer mechanical model of non-full-length bonded anchor cables, considering that the slurry-sand-stone body often does not produce overall destruction during the sliding shear process, the influence of the anchoring section grouting body and the free section grouting body on the load transfer mode of the anchor cable system is considered, and the differential equations of the mechanical equilibrium relationship are obtained by taking microelement segments for the anchoring section grouting body and the free section grouting body.

4. The method for calculating stress distribution of a non-full-length bonded anchor cable during the sliding extension stage according to claim 1, characterized in that: According to the analysis of the test results of the mechanical properties of the slurry-soil interface, the shear mechanical relationship of the slurry-soil interface is assumed to be an ideal line elastoplastic model, the shear failure strength formula of the slurry-soil interface is defined, and the tangential stress state of the slurry-soil interface is obtained.

5. The method for calculating stress distribution of a non-full-length bonded anchor cable during the sliding extension phase according to claim 1, characterized in that: The slip extension stage of the slurry-soil interface is defined as follows: as the axial load continues to increase, the shear stress of the slurry-soil interface continues to increase. The maximum shear stress of the slurry-soil interface of the non-full-length bonded anchor appears at the junction of the free section and the anchoring section, and decreases monotonically toward both ends of the anchor. When the maximum shear stress of the interface exceeds its shear failure strength, the interface enters a plastic state, and the plastic zone develops toward both ends of the anchor as the axial load increases. The state when the slurry-soil interface produces a plastic zone but has not fully entered the plastic stage is called the slip extension stage.

6. The method for calculating stress distribution of a non-full-length bonded anchor cable during the sliding extension stage according to claim 1, characterized in that: Taking into account the different normal stresses of anchor cables with different layout types, the stress distribution laws of the inclined anchor cables and vertical anchor cables in the sliding extension stage are described separately. The inclined anchor cables have sufficient burial depth and belong to deep buried structures. The normal stresses of different cross sections do not change with position, so the shear failure strength of the slurry-soil interface of different cross sections of the anchor cables remains constant. According to the elastic and plastic zoning, the mechanical equilibrium relationship of different stress intervals is described.

7. Stress distribution calculation system for non-full-length bonded anchor cable during sliding extension stage, characterized in that: include: Mathematical model building module, used to analyze the stress of non-full-length bonded anchor cables, consider the influence of anchor section grouting and free section grouting on the load transfer mode of anchor cable system, and build the mechanical equilibrium differential equation of load transfer of non-full-length bonded anchor cables; The tangential force analysis module is used to analyze the tangential force state of the slurry-soil interface according to the test results of the mechanical properties of the slurry-soil interface; The stress distribution calculation module is used to calculate the stress distribution of different types of anchor cables when the slurry-soil interface is in the sliding extension stage for inclined anchor cables and vertical anchor cables based on the mechanical equilibrium differential equation and the tangential stress state of the slurry-soil interface; Among them, by analyzing the normal stress of different types of anchor cables and the stress distribution law of anchor cables in the sliding extension stage, the mechanical equilibrium differential equations in different stress intervals are described according to the elastic and plastic partitions, so as to complete the stress distribution calculation of different types of anchor cables, and analyze the stress distribution of the anchor rod according to the solution results, predict its stress state, and realize the later design parameter optimization and bearing capacity evaluation.

8. A computer program product, comprising a computer program, characterized in that When the computer program is executed by a processor, the method for calculating stress distribution in the sliding extension stage of a non-full-length bonded anchor cable as described in any one of claims 1 to 6 is implemented.

9. A non-transitory computer-readable storage medium, characterized in that: The non-transitory computer-readable storage medium is used to store computer instructions. When the computer instructions are executed by the processor, the method for calculating the stress distribution in the sliding extension stage of a non-full-length bonded anchor cable as described in any one of claims 1 to 6 is implemented.

10. An electronic device, characterized in that: include: A processor, a memory and a computer program; wherein the processor is connected to the memory, the computer program is stored in the memory, and when the electronic device is running, the processor executes the computer program stored in the memory so that the electronic device executes the method for calculating the stress distribution in the sliding extension stage of a non-full-length bonded anchor cable as described in any one of claims 1 to 6.

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